MULTIPLICATION OF WHOLE NUMBER AND DECIMAL

Back to: Mathematics Primary 5

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How do you multiply by one-digit number?

Multiply each digit by the one-digit number, starting with the ones place. Regroup when necessary.

EXAMPLE 1:

A great white shark can swim 2,900 miles on a single meal. If a great white shark eats 3 meals a day, it could swim 2,900 x 3 or 8,700 miles.

2,900

X 3

6,000                      Multiply 3 x 2,000.

+ 2,700                     Multiply 3 x 900.

8,700                      Add the partial products.

Multiples of 10, 100, and 1,000

EXAMPLE 2:

Find 3 x 7,000.

3 x 7 = 21                                         3 x 7 ones = 21

3 x 70 = 210                              3 x 7 tens = 210

3 x 700 = 2,100                         3 x 7 hundreds = 2,100

3 x 7,000 = 21,000           3 x 7 thousands = 21,000

3 x 7,000                                                                                      21,000

 

So, 3 x 7,000 is 21,000. Notice that this answer is 3 x 7 with three zeros at the end.

Multiply Two-Digit Numbers

EXAMPLE 3:

Find 6 x 38.

One Way: Distributive Property 6 x 38 = (6 x 30) + (6 x 8) =   180     +    48 =   228

Another Way: Partial Products 38 x 6 48              Multiply 6 x 8 + 180             Multiply 6 x 30 228             Add the partial products.

Another Way: Paper and Pencil

Step 1 Multiply the ones. 4 38 6 x 8 = 48 x 6 Regroup 48 ones as 228 4 tens and 8 ones.

 

MULTIPLY MULTI-DIGIT NUMBERS

You multiply multi-digit numbers the same way you multiply a two-digit number by one-digit number.

 

EXAMPLE 4:

Today is Laura’s birthday, and she is nine years old. There are 365 days in one year. How many days old is Laura?

To find how many days old Laura is, multiply the number of days in a year by the number of years. That is, find 365 x 9.

 

You can use partial products.

365

x 9

45                             Multiply 9 x 5.

540                             Multiply 9 x 60.

+ 2,700                               Multiply 9 x 300.

3,285

 

So, Laura is 3,285 days old.

Multiply Greater Numbers

 

EXAMPLE 4:

If 7,275 visitors go to a zoo every week, how many visitors go to the zoo in a year?

Find 7,275 x 52.

 

Step 1 Multiply the ones. Regroup if necessary.   7,275 X   52  14,5507,275 x2

Step 2 Multiply the tens.     7,275 X   52 14,550 363,7507,275 x 5

 

 

Step 3 Add the partial products. Check for reasonableness. 1 3 2 1 1 7,275 X   52 14,550 + 363,750 378,300                        7,275 x 52

 

So, the zoo gets 378,300 visitors in a year.

MULTIPLICATION OF DECIMAL

The number of digits AFTER a decimal point are called DECIMAL PLACES.

• . 5                               1 decimal place

0    .   7                              1 decimal place

0    .   2 4                           2 decimal places

 

We conclude that in multiplying decimals, the number of decimal places in the product of decimals is the sum of the number of decimal places in the factors.

EXAMPLE:     Multiply         a.        11.6 × 0.47                b.        73.07 × 0.95

Solution

1. 1  1  .  6                         1 decimal place

×  0 . 4    7                         2 decimal places

8   1    2

4  6   4

5 . 4   5    2                                  3 decimal places

 

1. 7 3 . 0 7

×   0 . 9  5

3  6  5  3   5

6 5  7  6  3

6 9  4  1  6   5

 

MULTIPLICATION OF DECIMAL BY 10, 100, 1000

EXAMPLE: Multiply 36.98 by 10, by 100, by 1000. Look for a pattern.

3 6 . 9 8                              3 6 . 9 8                                  3 6 . 9 8

1 0                                1  0 0                                1  0   0 0

3 6 9 .80                       3 6 9 8 .0 0                        3 6 9 8 0. 0 0

 

PATTERN USED

36. There is one zero in 10                       10 × 36.98 = 3 6 . 9 8 = 369.8

To multiply by 10 move the decimal point

One place to the right.

36. There are two 0s in 100                     100 × 36.98 = 3 6 . 9 8 = 3698.

To multiply by 100 move the decimal point

two places to the right.

• There are three 0s in 1000                100 × 36.98 = 3 6 . 9 8 0 = 36980.

To multiply by 1000 move the decimal point

three places to the right.

EXAMPLES:

1. A satellite is travelling at a speed of 3.87 kilometres per second. How far does he travel in 9.2 seconds?

Solution:

We multiply 3.87 km/s by 9.2 to find how far.

3 . 8 7

9.2

7  7  4

3 4 8 3

3 5.6 0 4

The satellite travels 35.604 km in 9.2 seconds.

2. A flea can jump about 130 times as high as its own height. A flea is about 0.16 centimeters tall. About how high can a flea jump?

Height of the flea = 0.16cm

How high it can jump? = 130 times it height

=  130  0.16

= 20.8

Tim runs 9 mph and it takes him 2.91 hours to finish a race. To the nearest tenth of a mile, how far does he run ?

In one hour he runs = 9miles

In 2.91 hours, he will run = 2.91    9

= 26.19

= 26.2 (nearest tenth)

 

Quiz

1. Multiply these decimals:   18 x 2.5  4 x 0.6 57 x 0.8

2. A photogragh of a plant that that is 0.42 millimetres long is enlarged 260 times for a science book. Estimate how long the plant is in the book.
3. A giant tortoise can travel at a speed of about 0.25 kilometres per hour. At this rate, how far can he travel in 2.5 hours?
4. A snail moves at a speed of 0.008 kilometres per hour. How far can it travel in 0.7 hours?
5. A weekly telephone call from Kaduna to Lagos might cost #60.45 for the first 3 minutes and #17.85 for each additional minute. How much will a 13 minute call cost?
6. A book has 142 lines on each page. If the book has 25 pages, find the total number of lines in the book.
7. Find the product of 625 and 48.

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